The wave functions were expanded in a plane-wave basis truncated at 600 eV. For SrCoO\(_3\)  and SrIrO\(_3\)  a 20-atom unit cell was used (\(\sqrt{2}a\)\(\times \)\(\sqrt{2}a\)\(\times \)\(2c\) ), whereas a 40-atom unit cell was employed for Sr\(_2\) CoIrO\(_6\)  in a \(2a\)\(\times \)\(2a\)\(\times \)\(2c\)  setup in order to model the cation and magnetic arrangement (see Fig. REF ). To sample the Brillouin zone, 8\(\times \) 8\(\times \) 6 \(k\) -points shifted off \(\Gamma \)  were generated using the Monkhorst-Pack scheme [1]} for SrCoO\(_3\)  and SrIrO\(_3\) , and 5\(\times \) 5\(\times \) 5 \(k\)  points were used for the double perovskite Sr\(_2\) CoIrO\(_6\) . The convergence criterion for the self-consistent calculation is 10\(^{-6}\)  eV for the total-energy. A Fermi smearing of 0.05 eV is used for the geometry optimization and the further analysis. For SrCoO\(_3\)  and SrIrO\(_3\) , all atomic positions and unit cell parameters were optimized until the atomic forces were less than 0.01 eV/Å. For the strained DP Sr\(_2\) CoIrO\(_6\)  all atomic positions and the \(c\) -lattice constant were optimized.
